A unifying approach to risk-measure-based optimal reinsurance problems with practical constraints

Abstract

The design of optimal reinsurance treaties in the presence of multifarious practical constraints is a substantive but underdeveloped topic in modern risk management. To examine the influence of these constraints on the contract design systematically, this article formulates a generic constrained reinsurance problem where the objective and constraint functions take the form of Lebesgue integrals whose integrands involve the unit-valued derivative of the ceded loss function to be chosen. Such a formulation provides a unifying framework to tackle a wide body of existing and novel distortion-risk-measure-based optimal reinsurance problems with constraints that reflect diverse practical considerations. Prominent examples include insurers' budgetary, regulatory and reinsurers' participation constraints. An elementary and intuitive solution scheme based on an extension of the cost-benefit technique in Cheung and .] is proposed and illuminated by analytically identifying the optimal risk-sharing schemes in several concrete optimal reinsurance models of practical interest. Particular emphasis is placed on the economic implications of the above constraints in terms of stimulating or curtailing the demand for reinsurance, and how these constraints serve to reconcile the possibly conflicting objectives of different parties. ARTICLE HISTORY

Optimal XL-insurance under Wasserstein-type ambiguity

“…The retained loss that still needs to be covered by the insured entity is X − I(X) + π g,θ (I(X)). For the set of admissible contracts, we follow the same line as Cheung et al (2012), Chi and Tan (2013), Lo (2017b) and consider the set of feasible contracts of the form…”

A Neyman-Pearson Perspective on Optimal Reinsurance With Constraints

“…i. The construction of the optimal solutions in Case (b) of Theorem 3.2 can be demystified by the dissection analysis performed in Lo (2016), which can be summarized as follows. Observe that the set { f 1 < c * f 0 } can be partitioned into…”

“…Explicitness and completeness of solutions: Arguably, the greatest strength of the Neyman-Pearson approach is its ability to exhibit the optimal solutions of a wide spectrum of constrained optimal reinsurance problems in explicit and easily comprehensible forms, as opposed to the nebulous solutions often accompanied by several implicitly defined quantities observed in many existing papers (e.g., Cai et al, 2016;Lu et al, 2016). In addition, with explicit solutions beyond the classical insurance-layer-type solutions identified, our approach manages to provide full characterizations of the optimal solutions and thoroughly address the feasibility, well-posedness and uniqueness issues of optimal reinsurance problems, which are unsettled in most papers (e.g., Cai et al, 2016;Lo, 2016;Lu et al, 2016).…”

Optimal Reinsurance From the Viewpoints of Both an Insurer and a Reinsurer Under the Cvar Risk Measure and Vajda Condition

“…Cai and Weng (2016) studied optimal reinsurance with the expectile. For more studies about optimal reinsurance under risk measures, we refer to Zheng and Cui (2014), Assa (2015), Lo (2017aLo ( , 2017b, etc. Most of the results obtained are from the insurer's point of view or from the reinsurer's point of view.…”